Random Lie-point symmetries

Abstract

We introduce the notion of a random symmetry. It consists of taking the action given by a deterministic flow that maintains the solutions of a given differential equation invariant and replacing it with a stochastic flow. This generates a random action, which we call a random symmetry.

Lie-Point Symmetries and Backward Stochastic Differential Equations

“…The transformations of the Wiener process w(t) intow(t) is specifically discussed in Appendix A in [6]. For more details about this transformation, the readers can also refer to [11,21,22], etc.…”

“…Since then many papers contribute to this area. The symmetries includes fiber preserving symmetry, generalized Lie-point symmetry, W-symmetry ( [9,10]), and random Lie symmetry [11], etc. They are mostly applied in Itô SDE driven by Brownian motion.…”